Maple 2016 Questions and Posts

These are Posts and Questions associated with the product, Maple 2016

Please I found out that the MatrixInverse on the assignment statement P3 does not run for about three days now. Please kindly help to simplify the code. Thank you and kind regards.

restart; omega := v/h;
r := a[0]+a[1]*x+a[2]*sinh(omega*x)+a[3]*cosh(omega*x)+a[4]*cos(omega*x)+a[5]*sin(omega*x);
b := diff(r, x);

c := eval(b, x = q) = f[n];
d := eval(r, x = q+3*h) = y[n+3]; e := eval(b, x = q+3*h) = f[n+3];
g := eval(b, x = q+2*h) = f[n+2];
i := eval(b, x = q+h) = f[n+1];
j := eval(b, x = q+4*h) = f[n+4];
k := solve({c, d, e, g, i, j}, {a[0], a[1], a[2], a[3], a[4], a[5]});
Warning,  computation interrupted
assign(k);
cf := r;
s4 := y[n+4] = simplify(eval(cf, x = q+4*h));
s3 := y[n+2] = simplify(eval(cf, x = q+2*h));
s2 := y[n+1] = simplify(eval(cf, x = q+h));
s1 := y[n] = simplify(eval(cf, x = q));

with(LinearAlgebra);
with(plots);
h := 1;
YN_1 := seq(y[n+k], k = 1 .. 4);
A1, a0 := GenerateMatrix([s1, s2, s3, s4], [YN_1]);
eval(A1);
YN := seq(y[n-k], k = 3 .. 0, -1);
A0, b1 := GenerateMatrix([s1, s2, s3, s4], [YN]);
eval(A0);
FN_1 := seq(f[n+k], k = 1 .. 4);
B1, b2 := GenerateMatrix([s1, s2, s3, s4], [FN_1]);
eval(B1);
FN := seq(f[n-k], k = 3 .. 0, -1);
B0, b3 := GenerateMatrix([s1, s2, s3, s4], [FN]);
eval(B0);
ScalarMultiply(R, A1)-A0;
det := Determinant(ScalarMultiply(R, A1)-A0);
P1 := A1-ScalarMultiply(B1, z);
P2 := combine(simplify(P1, size), trig);
P3 := MatrixInverse(P2);
P4 := A0-ScalarMultiply(B0, z);
P5 := MatrixMatrixMultiply(P3, P4);
P6 := Eigenvalues(P5);
f := P6[4];
T := unapply(f, z);
implicitplot(f, z = -5 .. 5, v = -5 .. 5, filled = true, grid = [5, 5], gridrefine = 8, labels = [z, v], coloring = [blue, white]);

 

Hello,

I want to sort the formulae to Psi and Beta, but I don't know how it works. I have tried it with sort, simplify, isolate, but that isn't what I'm searching.

It should looks like the simplier formula in the picture.

 

ab := (diff(Psii(t), t, t))*J-l[f]*(F[s, f, l]+F[s, f, r])+l[r]*(F[s, r, l]+F[s, r, r])-(1/2)*b[r]*(-F[s, r, l]*delta[l]+F[s, r, r]*delta[r]) = 0;
  / d  / d         \\                                   
  |--- |--- Psii(t)|| J - l[f] (F[s, f, l] + F[s, f, r])
  \ dt \ dt        //                                   

     + l[r] (F[s, r, l] + F[s, r, r])

       1                                                      
     - - b[r] (-F[s, r, l] delta[l] + F[s, r, r] delta[r]) = 0
       2                                                      
bc := (diff(betaa(t), t, t))*m*v*betaa(t)+F[s, r, l]*delta[l]+F[s, r, r]*delta[r]-(diff(Psii(t), t)) = 0;
    / d  / d          \\                                   
    |--- |--- betaa(t)|| m v betaa(t) + F[s, r, l] delta[l]
    \ dt \ dt         //                                   

                               / d         \    
       + F[s, r, r] delta[r] - |--- Psii(t)| = 0
                               \ dt        /    
cd := (diff(betaa(t), t))*m*v+F[s, r, l]+F[s, r, r]+F[s, f, l]+F[s, f, r]-(diff(Psii(t), t)) = 0;
   / d          \                                           
   |--- betaa(t)| m v + F[s, r, l] + F[s, r, r] + F[s, f, l]
   \ dt         /                                           

                     / d         \    
      + F[s, f, r] - |--- Psii(t)| = 0
                     \ dt        /    
F[s, f, l] := c[fl]*alpha[fl];
                        c[fl] alpha[fl]
F[s, f, r] := c[fr]*alpha[fr];
                        c[fr] alpha[fr]
F[s, r, l] := c[rl]*alpha[rl];
                        c[rl] alpha[rl]
F[s, r, r] := c[rr]*alpha[rr];
                        c[rr] alpha[rr]
alpha[fl] := (-v*betaa-l[f]*(diff(Psii(t), t)))/(-v+(1/2)*b[f]*(diff(Psii(t), t)));
                                 / d         \
                 -v betaa - l[f] |--- Psii(t)|
                                 \ dt        /
                 -----------------------------
                        1      / d         \  
                   -v + - b[f] |--- Psii(t)|  
                        2      \ dt        /  
alpha[fr] := (-v*betaa-l[f]*(diff(Psii(t), t)))/(v-(1/2)*b[f]*(diff(Psii(t), t)));
                                 / d         \
                 -v betaa - l[f] |--- Psii(t)|
                                 \ dt        /
                 -----------------------------
                       1      / d         \   
                   v - - b[f] |--- Psii(t)|   
                       2      \ dt        /   
alpha[rl] := delta[l]+(-v*betaa+l[r]*(diff(Psii(t), t)))/(-v+(1/2)*b[r]*(diff(Psii(t), t)));
                                       / d         \
                       -v betaa + l[r] |--- Psii(t)|
                                       \ dt        /
            delta[l] + -----------------------------
                              1      / d         \  
                         -v + - b[r] |--- Psii(t)|  
                              2      \ dt        /  
alpha[rr] := delta[r]+(-v*betaa+l[r]*(diff(Psii(t), t)))/(-v-(1/2)*b[r]*(diff(Psii(t), t)));
                                       / d         \
                       -v betaa + l[r] |--- Psii(t)|
                                       \ dt        /
            delta[r] + -----------------------------
                              1      / d         \  
                         -v - - b[r] |--- Psii(t)|  
                              2      \ dt        /  


ab;
                             /
                             |
/ d  / d         \\          |
|--- |--- Psii(t)|| J - l[f] |
\ dt \ dt        //          |
                             |
                             \

        /                / d         \\
  c[fl] |-v betaa - l[f] |--- Psii(t)||
        \                \ dt        //
  -------------------------------------
             1      / d         \      
        -v + - b[f] |--- Psii(t)|      
             2      \ dt        /      

           /                / d         \\\        /      /      
     c[fr] |-v betaa - l[f] |--- Psii(t)|||        |      |      
           \                \ dt        //|        |      |      
   + -------------------------------------| + l[r] |c[rl] |delta[
               1      / d         \       |        |      |      
           v - - b[f] |--- Psii(t)|       |        |      |      
               2      \ dt        /       /        \      \      

                       / d         \\
       -v betaa + l[r] |--- Psii(t)||
                       \ dt        /|
  l] + -----------------------------|
              1      / d         \  |
         -v + - b[r] |--- Psii(t)|  |
              2      \ dt        /  /

           /                           / d         \\\          /
           |           -v betaa + l[r] |--- Psii(t)|||          |
           |                           \ dt        /||   1      |
   + c[rr] |delta[r] + -----------------------------|| - - b[r] |
           |                  1      / d         \  ||   2      |
           |             -v - - b[r] |--- Psii(t)|  ||          |
           \                  2      \ dt        /  //          \
       /                           / d         \\         
       |           -v betaa + l[r] |--- Psii(t)||         
       |                           \ dt        /|         
-c[rl] |delta[l] + -----------------------------| delta[l]
       |                  1      / d         \  |         
       |             -v + - b[r] |--- Psii(t)|  |         
       \                  2      \ dt        /  /         

           /                           / d         \\         \   
           |           -v betaa + l[r] |--- Psii(t)||         |   
           |                           \ dt        /|         |   
   + c[rr] |delta[r] + -----------------------------| delta[r]| = 
           |                  1      / d         \  |         |   
           |             -v - - b[r] |--- Psii(t)|  |         |   
           \                  2      \ dt        /  /         /   

  0
bc;
 / d  / d          \\             
 |--- |--- betaa(t)|| m v betaa(t)
 \ dt \ dt         //             

            /                           / d         \\         
            |           -v betaa + l[r] |--- Psii(t)||         
            |                           \ dt        /|         
    + c[rl] |delta[l] + -----------------------------| delta[l]
            |                  1      / d         \  |         
            |             -v + - b[r] |--- Psii(t)|  |         
            \                  2      \ dt        /  /         

            /                           / d         \\         
            |           -v betaa + l[r] |--- Psii(t)||         
            |                           \ dt        /|         
    + c[rr] |delta[r] + -----------------------------| delta[r]
            |                  1      / d         \  |         
            |             -v - - b[r] |--- Psii(t)|  |         
            \                  2      \ dt        /  /         

      / d         \    
    - |--- Psii(t)| = 0
      \ dt        /    
cd;
 / d          \    
 |--- betaa(t)| m v
 \ dt         /    

            /                           / d         \\
            |           -v betaa + l[r] |--- Psii(t)||
            |                           \ dt        /|
    + c[rl] |delta[l] + -----------------------------|
            |                  1      / d         \  |
            |             -v + - b[r] |--- Psii(t)|  |
            \                  2      \ dt        /  /

            /                           / d         \\
            |           -v betaa + l[r] |--- Psii(t)||
            |                           \ dt        /|
    + c[rr] |delta[r] + -----------------------------|
            |                  1      / d         \  |
            |             -v - - b[r] |--- Psii(t)|  |
            \                  2      \ dt        /  /

            /                / d         \\
      c[fl] |-v betaa - l[f] |--- Psii(t)||
            \                \ dt        //
    + -------------------------------------
                 1      / d         \      
            -v + - b[f] |--- Psii(t)|      
                 2      \ dt        /      

            /                / d         \\                    
      c[fr] |-v betaa - l[f] |--- Psii(t)||                    
            \                \ dt        //   / d         \    
    + ------------------------------------- - |--- Psii(t)| = 0
                1      / d         \          \ dt        /    
            v - - b[f] |--- Psii(t)|                           
                2      \ dt        /                           
 

 

 

 

Imagine a brachistochrone shaped path made of a frictionless flexible metal strip which reacts to the force of a weighty sliding object.

Depending on its flexibility and the object's mass, what would be the strip's initial shape for fastest descent between its top and bottom? How would its shape change during the object's descent?

Perhaps an aircraft emergency escape slide or the fastest path for a slalom skier exemplify this kind of situation.

Hello,

I want to write a code about numerical solving N(for example N=150) coupled differential equations (ODE ) with M boundary conditions in Maple but I do not know how to do it and I cannot find anything useful. in particular, I have trouble inserting boundary conditions which are a lot for N coupled difrential equations.

Does somebody have a code script on this matter? please let me know.

Thanks a bounch in advance.

Hello everyone!

I'm interesting in "zcoloring" funciton in colorscheme option.

I wrote simple programm which compares two results: spectrogram of signal drawn with "colormap" list and spectrogram which was plotted with zcoloring function. I use red, green, blue functions to construct JET-colormap: list and expressions in "zcoloring".

My result:

As I understand, when I use:

colorscheme = ["zcoloring", [z-> Red color function(z), z-> Green color function(z), z-> Blue color function(z)], colorspace = "RGB"]

Maple plots z-value with color RGB color coordinates defined from "zcoloring". For example, if "zcoloring" is

colorscheme = ["zcoloring", [z-> 5*z, z-> 3*z, z-> 2*z], colorspace = "RGB"]

and z value is 10, then 10 value will correspond [50,30,20]-RGB color.

My test program:

Spectrogram_zcoloring.mw

Spectrogram of my test signal:

list_test.txt

Basically it spits out the subset of values for which a division by zero error will occur for the function you specify on  range you specify for each of it's arguments, but I get an ambigous error when ever exponentiation features in the function I specify, which of course dramatically reduces the application of the calculator. Division,addition,substraction and multiplication are currently the only available arithmetic operators availble for the function window that I know the error will not occur.

If some one can help it is much appriciated

 

DIVISION_BY_ZERO_CALCULATOR.mw

Is there something I should be doing whenever I use simplify to avoid things like this, or should I stop using the "is" function all together?

 

interface(showassumed = 0):

 

sum(binomial(k+j, k), j = 0 .. n-k) = binomial(n+1, k+1)

(n-k+1)*binomial(n+1, k)/(k+1) = binomial(n+1, k+1)

(1)

#And we have:
is(sum(binomial(k+j, k), j = 0 .. n-k) = binomial(n+1, k+1))

FAIL

(2)

#And since:
is(simplify(convert(sum(binomial(k+j, k), j = 0 .. n-k) = binomial(n+1, k+1), 'factorial')))

true

(3)

is(sum(binomial(k+j, k), j = 0 .. n-k) = binomial(n+1, k+1)) = is(simplify(convert(sum(binomial(k+j, k), j = 0 .. n-k) = binomial(n+1, k+1), 'factorial')))


 

Download main.mw

I was trying to learn more about the commands in this package and found it to be someone non satisfying:


 

Download sockets_strangeness.mw

 

I am trying to solve a simple two-equation linear system with solve, but I keep getting this weird result where the magnitude order of the numerator and denominator don't cancel out. Whenever I have a linear system with floating-point numbers, more unknowns than equations and try to solve it for a specific set of variables, this happens.

Any suggestions on how to get around this? Or do I need to solve it manually?

Hi, my codes ran smoothly well until I changed some assignment value. It reported invalid object error.

Error, Got internal error in Typesetting:-Parse:-Postprocess : "internal error: invalid object "

Part of the codes are as follows:

""sigma:=0.00002:    m:=5:   n:=4:
Error, Got internal error in Typesetting:-Parse:-Postprocess : "internal error: invalid object "

Could anyone give some hints on what goes wrong here? It seems to be a configuration issue but I completely have no clue..

Thanks a million in advance,

Best,

Jie

 

 

The worksheet below rolls an ellipse along the y axis with constant energy.

How can the physics be enhanced to roll the ellipse along a non-linear curve (e.g. a sine curve) with constant energy?

EllipseRoll.mw

Help create file Excel in ExcelTools, but error row 564?

thu_file.mw

Please help me? 

I have a physics question I need to program it by Maple , Can you help me to solve ? Its Problem 9.34 from Griffiths

Hey there,

I'm trying to numerically intergrate a function s(K,i,j) dK using runge kutta over a 2D grid of i,j values. Essentialy, performing the same sort of integral many different times for slightly different combinations of i and j. The function is more or less gaussian, and so the bulk of the result will come from the values of K around the peak of said gaussian. For some combinations of i and j, the function seems to have a singularity on the right edge of the gaussian peak, which causes my script to spit out an error, telling me the calculation cannot be performed further to the right past the singularity. Now, like i said before, the singularity is on the very edge of the gaussian and therefore I am perfectly happy to stop the integration before the singularity, because anything past it wont contribute very much to the result.

How can I use dsolve events to halt my integration just before hitting the singularity?

RK := (i, j) -> dsolve({diff(n(K), K) = K*s(K, a[i], b[j]), n(0) = 0}, numeric, method = rkf45)

 

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